Question

Julian is trying to find the height of a radio antenna on the roof of a local

building. He stands at a horizontal distance of 28 meters from the building.
The angle of elevation from his eyes to the roof (point A) is 32°, and the
angle of elevation from his eyes to the top of the antenna (point B) is 35°. If
his eyes are 1.51 meters from the ground, find the height of the antenna (the
distance from point A to point B). Round your answer to the nearest tenth of
a meter if necessary.

Answer 1

2.1 meters

Explanation:

You want the height of a radio antenna that has an angle of elevation of 32° to its base (A) from a point at a horizontal distance of 28 meters, and an angle of elevation of 35° to its top (B) from the same point.

Tangent

The tangent relation tells you that ...

Tan = Opposite/Adjacent

In the geometry of this problem, the angles are the angles of elevation, and the opposite side is the height from eye level to the corresponding points A or B.

tan(32°) = height of A / (28 m)

height of A = (28 m)tan(32°)

Similarly, ...

height of B = (28 m)tan(35°)

Antenna height

The height of the antenna is the difference of these heights:

antenna height = (height of B) - (height of A)

antenna height = (28 m)·tan(35°) -(28 m)·tan(32°)

antenna height = (28 m)·(tan(35°) -tan(32°)) ≈ 2.1 m

The height of the antenna is about 2.1 meters.

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